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Trigonometry: Polar and Rectangular Coordinates

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Convert the equation to polar coordinates and simplify.
1. a. xy = 1
b. (x^2 + y62)^2 = 2xy

Express the equation in rectangular coordinates.
2. a. r = 3sin(t)
b. r = 4cos3(t)
r^2 = 4sin2(t)
r = 4/(2 + cos(t))

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Solution Summary

This solution converts the first equation to polar coordinates and simplifies it, and expresses the second equation in rectangular coordinates.

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1. First x=rcos(t), y=rsin(t).
a. Xy=1.
(rcos(t))(rsin(t))=1
r^2(cos(t)sin(t)=1
r^2sin(2t)=2.
Therefore, the polar equation is r^2sin(2t)=2.

b. Since x^2+y^2=r^2
(r^2)^2=2r^2cos(t)sin(t),
We first cancel out r^2: r^2=sin(2t).
Therefore, the polar equation is ...

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